Reference voltage supplies are required in a wide variety of electronic systems to provide a known value of voltage to which a signal of interest may be compared to. The most common application is as the reference voltage input for a comparator to determine if a signal of interest has attained or exceeded some predetermined value.
A bandgap reference is typically designed around known base-emitter characteristics of bipolar transistors to provide circuit parameters suitable for this application. Manufacturing processes for bipolar transistors are also stable and easily manipulated to provide a wide range of transistor performance parameters that are independent of temperature.
The bandgap type of reference supply provides a high accuracy, temperature-compensated or temperature-independent output voltage that, ideally, is directly proportional to only the energy-bandgap voltage of the semiconductor material in a bipolar transistor. To realize the ideal condition requires compensating for or canceling the non-linear characteristics of a transistor circuit that are temperature dependent, which is referred to as curvature correction.
The temperature dependence of a bandgap reference can be seen in the equation for the base-emitter voltage of a forward-biased bipolar transistor: ##EQU1## where: V.sub.g0 is the energy-bandgap voltage at zero degrees Kelvin,
T.sub.R is a reference temperature, PA1 T is the operating temperature of the transistor, PA1 V.sub.BE-T.sbsb.R is the base-emitter voltage at temperature T.sub.R, PA1 n is a process-dependent but temperature-independent variable, PA1 x relates to the exponential order for the temperature-dependent collector current of the transistor, i.e., I.sub.C T.sup.X, PA1 k is Boltzmann's constant, and PA1 q is the electrical charge of an electron. PA1 I.sub.C is the collector current of an NPN transistor, PA1 J.sub.S is the saturation current density, and PA1 A is the emitter area. PA1 V.sub.T is given by the equation: ##EQU4## where: K is Boltzmann's constant, PA1 T is the operating temperature of the transistor, and PA1 q is the electrical charge of an electron.
It can be seen from this equation that the transistor's base-to-emitter voltage is inherently non-linear with temperature due to the logarithmic term that contains the ratio of the two temperatures.
Bandgap references are usually referred to as having first or second order compensation. A first order type is one whose design addresses only the linear terms in Equation (1), with the remaining terms being ignored. A second order type is one whose design is able to overcome some of the non-linearity associated with the logarithmic term in Equation (1) in addition to addressing the linear terms.
The operation of a bandgap reference typically requires summing two voltages, the first of which is base-emitter dependent in accordance with Equation (1), and the second of which is dependent upon a proportional to absolute temperature (PTAT) current. The summation of the two voltages is utilized in achieving the curvature correction, as will be presented below.
FIG. 1 is a schematic diagram for a PTAT current generator arrangement that utilizes a PTAT generator, comprising NPN transistors Q1 and Q2, resistor R1, and an active current mirror circuit CM1. The current mirror circuit CM1 forces the collector currents of transistors Q1 and Q2 to be equal which is shown as I.sub.c in signal lines S1 and S2. If the small base current of Q1 is ignored it can be seen in FIG. 1 that: ##EQU2##
The base-emitter voltage for transistors Q1 and Q2 is given by the equation : ##EQU3## where: V.sub.T is a thermal voltage,
Substituting equations (3) and (4) into Equation (2) yields: ##EQU5##
Expanding Equation (5) yields: ##EQU6##
The saturation current density J.sub.S and emitter area A for a given transistor are constant, as are R1, K, and q. The first and third logarithmic terms cancel each other, and the second and fourth logarithmic terms are constants.
Equation (6) may therefore be simplified to: EQU I.sub.C =(constant).times.T=I.sub.PTAT, Eq. (7)
making the collector current of Q1 in FIG. 1 directly proportional to absolute temperature T. This current is mirrored by current mirror CM1 to signal line S4 as I.sub.PTAT.
The circuit of FIG. 1 is included in a preferred embodiment of the invention shown in discussion below. Variations of this circuit are also used in the known art to establish a circuit current that is dependent only on absolute temperature.
FIG. 2 is an example of the prior art and is a partial schematic for a first order bandgap reference that sums a PTAT voltage and a diode junction voltage to arrive at a partially compensated output reference voltage. The output reference voltage is given by: EQU V.sub.REF =V.sub.PTAT +V.sub.D =I.sub.PTAT R2 +V.sub.D. Eq. (8)
The diode voltage, V.sub.D, can be characterized by Equation (1) presented earlier, and I.sub.PTAT varies only with temperature in accordance with Equation (7). The PTAT voltage increases linearly with temperature and partially offsets the negative influence of V.sub.D.
The overall performance of the bandgap reference of FIG. 2 can be understood from FIG. 3. This figure illustrates the temperature dependence of both the PTAT voltage and diode voltage, and the resulting output reference voltage. The curve labeled V.sub.D is derived from Equation (1) and reflects the increasingly nonlinear influence with temperature of the logarithmic term. The curve labeled V.sub.PTAT is derived from I.sub.PTAT R2 and is linear with temperature. The curve labeled V.sub.REF is the resultant output reference voltage in FIG. 2 and shows the effect of summing the PTAT voltage with the diode junction voltage.
It can be seen that the first order bandgap reference of FIG. 2 exhibits considerable non-linearity with temperature, but would be suitable over a limited temperature range.
FIG. 4 is another example of the prior art and is a partial schematic for a second order bandgap reference that sums a base-to-emitter voltage of a transistor, a PTAT voltage, and a squared PTAT voltage to arrive at the output reference voltage: EQU V.sub.REF =V.sub.BE3 +2I.sub.PTAT (R3+R4)+I.sup.2.sub.PTAT R4.Eq. (9)
Voltage V.sub.BE3 can be characterized by Equation (1), and I.sub.PTAT varies linearly with temperature in accordance with Equation (7). The collector currents of transistors Q3 and Q4 are equal by virtue of the current mirror circuit CM2. The squared PTAT voltage, I.sup.2.sub.PTAT R4, in Equation (9) serves to offset the increasingly negative V.sub.BE3 as the operating temperature of the circuit increases.
The performance of the circuit in FIG. 4 is illustrated in FIG. 5, which is similar to FIG. 3 with the addition of the curve labeled V.sup.2.sub.PTAT. The effect of the squared PTAT voltage on circuit performance can be seen by comparing the curves labeled V.sub.REF in FIGS. 3 and 5. The variation of V.sub.REF in FIG. 5 is much less pronounced with temperature variations than that in FIG. 3 due to the use of I.sup.2.sub.PTAT in the circuit of FIG. 4.